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Ben Webster
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Yes. Use Plucker embedding to embed it into $CP^n$ then restrict Fubini-SturdyStudy metric.

Yes. Use Plucker embedding to embed it into $CP^n$ then restrict Fubini-Sturdy metric.

Yes. Use Plucker embedding to embed it into $CP^n$ then restrict Fubini-Study metric.

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Bugs Bunny
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Yes. Use Plucker embedding to embed it into $CP^n$ then restrict Fubini-Sturdy metric.